Proves representability of complex semigroup systems.
problem Representability of systems of proportionally modular numerical semigroups.
method Canonical equivariant resolution of weighted homogeneous surface singularities.
result Every system of proportionally modular numerical semigroups is representable.
CNN improves medium-range temperature forecasts with limited resources.
problem Limited computational resources for high-resolution temperature forecasts.
method CNN post-processing with ensemble NWP models for bias correction and spatial downscaling.
result High-resolution (5-km) surface temperature forecasts with lead times up to 5.5 days.
The paper presents a method to recover high-resolution signals from low-resolution measurements.
problem Recovering high-resolution signals from low-resolution indirect measurements.
method Combining generalized sampling and functional principal component analysis.
result High-resolution recovery is possible under certain conditions and with a sufficiently large training set.
We present a method of generating high resolution 3D shapes from natural language descriptions. To achieve this goal, we propose two steps that generating low resolution shapes which roughly reflect texts and generating high resolution shapes which reflect the detail of texts. In a previous paper, the authors have show…
Probabilistic SR method speeds up high-fidelity simulations with reliable uncertainty estimates.
problem Lack of reliable uncertainty quantification in deep-learning based SR methods.
method Statistical Finite Element Method and energy-based generative modeling.
result Efficient high-resolution predictions with inherent uncertainty estimates.
We generalise Simpson's nonabelian Hodge correspondence to the context of projective varieties with klt singularities. The proof relies on a descent theorem for numerically flat vector bundles along birational morphisms. In its simplest form, this theorem asserts that given any klt variety X and any resolution of singu…
Super-resolution is a classical problem in image processing, with numerous applications to remote sensing image enhancement. Here, we address the super-resolution of irregularly-sampled remote sensing images. Using an optimal interpolation as the low-resolution reconstruction, we explore locally-adapted multimodal conv…
The shortage of high-resolution urban digital elevation model (DEM) datasets has been a challenge for modelling urban flood and managing its risk. A solution is to develop effective approaches to reconstruct high-resolution DEMs from their low-resolution equivalents that are more widely available. However, the current …
The paper solves complex control problems using neural networks.
problem Solving McKean-Vlasov control problems.
method Mean-field neural networks and algorithms based on dynamic programming and stochastic maximum principle.
result Extensive numerical results show the accuracy of the proposed algorithms.
Deep generative models improve global precipitation forecasts.
problem Accurately forecasting extreme rainfall is challenging and costly.
method Trained a Conditional Generative Adversarial Network (CorrectorGAN) to correct and super-resolve global precipitation forecasts.
result CorrectorGAN produces high-resolution, bias-corrected forecasts in seconds.
Novel neural network solves PDEs with multi-scale resolution.
problem Solving time-dependent PDEs with varying spatial and temporal scales.
method Multi-scale message passing neural network with temporal and spatial gating modules.
result Outperforms baselines on PDEs with diverse scales.
Bayesian framework for identifying localized regions of interest in dynamical systems.
problem Identifying regions of high-resolution uncertainty quantification in complex dynamical systems.
method Bayesian inference with Gaussian process surrogate and polynomial chaos expansion.
result Unified computational scheme reduces overall cost for uncertainty quantification.
Physics-informed neural operator learns from coarse to fine discretized data.
problem Lack of high-fidelity training data and uneven grid resolution.
method Physics-informed multi-resolution neural operator framework.
result Learn from arbitrarily discretized input functions using latent embedding and finite difference solver.
The extension of the classical Bayesian penalized spline method to inference on vector-valued functions is considered, with an emphasis on characterizing the suitability of the method for general application.We show that the standard quadratic penalty is exactly analogous to the energy of a stretched string, with the p…
This research accelerates sampling methods using Nesterov's Acceleration.
problem Improving sampling efficiency in MCMC methods.
method Developed a Hessian-Free High-Resolution ODE reformulation of NAG-SC, injected noise, and discretized the diffusion process.
result Quantified acceleration beyond underdamped Langevin in W2 distance for log-strongly-concave targets. A new method generates mixed-type features in tabular data with improved realism and accuracy.
problem Generating mixed-type features combining discrete and continuous data is challenging.
method A cascaded approach: first generates low-resolution categorical and coarse numerical features, then uses these in a high-resolution flow matching model.
result The model significantly improves detection scores, generating more realistic samples and capturing distributional details.
New insights into RL efficiency from managing time discretization.
problem The impact of time discretization on RL methods in continuous-time systems.
method Analysis of Monte-Carlo policy evaluation for LQR systems.
result An optimal choice of temporal resolution for a given data budget improves policy evaluation efficiency.
We introduce a new, systematic framework for visualizing information flow in deep networks. Specifically, given any trained deep convolutional network model and a given test image, our method produces a compact support in the image domain that corresponds to a (high-resolution) feature that contributes to the given exp…
Probabilistic pseudo knots model uncertain knot diagrams.
problem Modeling knots with unresolved crossings.
method Assign probabilities to undetermined crossings; define probabilistic equivalence and extend classical knot invariants.
result Capture uncertainty in physical, biological, and computational contexts.
Deep learning predicts curvature of 2D interfaces in level-set method.
problem Estimating curvature in level-set method for complex interfaces.
method Deep learning using feed-forward neural networks trained on synthetic data.
result Deep learning models approximate curvature with comparable precision to traditional methods.
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data o…
A new numerical framework simplifies elastic surface matching and comparison.
problem Challenging problem in surface comparison and matching in computer vision.
method Relaxing the geodesic boundary constraint using a varifold fidelity metric.
result Flexibility to deal with arbitrary topologies and sampling patterns, scalability to large meshes.
The study optimizes Gaussian process approximations for finite-rank models.
problem Posterior behavior of finite-rank approximations differs from parent GP priors.
method Locally supported basis expansions with dependent Gaussian coefficients.
result Finite-rank expansions inherit the same posterior contraction rate as parent GP priors.
A new autoencoder architecture captures multiscale data.
problem Multiscale spatio-temporal data representation.
method Integrates multigrid methods, convolutional autoencoders, and transfer learning.
result Adaptive, hierarchical architecture captures different scaled features dynamically.
DL improves precipitation nowcasting from radar images.
problem Precise short-term precipitation predictions for extreme weather adaptation.
method Image-to-image translation using UNET CNN, compared to optical flow, persistence, and HRRR.
result UNET-based DL outperforms traditional models in 1 km x 1 km, 1 hour precipitation nowcasting.
SC-Net learns interpretable filters for inverse problems, achieving optimal convergence and super-resolution.
problem Solving ill-posed inverse problems with effective regularization and interpretability.
method SC-Net operates in the spectral domain, learning a pointwise adaptive filter function based on signal-to-noise ratio.
result SC-Net achieves optimal convergence rate and zero-shot super-resolution, matching theoretical bounds.
Study identifies numerical signs of blow-up in hydrodynamic equations.
problem Determining if numerical results of blow-up are genuine or artifacts.
method Geometrically consistent spatiotemporal discretization of complexified Euler equations.
result Identification of a signature based on supremum norm growth rates of vorticity.
Machine learning and deep learning infer surface/groundwater exchange from temperature data.
problem Inferring surface/groundwater exchange from temperature data with high temporal resolution.
method Application of machine learning and deep learning algorithms to infer surface/groundwater exchange flux from subsurface temperature observations.
result DL methods outperform ML methods in interpreting noisy temperature data, especially with a smoothing filter.
Method infers assortative communities in networks without resolution limit.
problem Finding statistically significant assortative modules in networks.
method Nonparametric Bayesian formulation of the planted partition model.
result Method uncovers an arbitrarily large number of communities with statistical evidence.
MetNet forecasts precipitation up to 8 hours with high spatial and temporal resolution.
problem Precise weather forecasting for long lead times.
method Neural network architecture using axial self-attention for global context aggregation.
result MetNet outperforms Numerical Weather Prediction at forecasts of up to 8 hours.
This study analyzes costs of CCP default resolution using Radner equilibrium approach.
problem Analyzing costs of CCP default resolution for investment banks' derivatives.
method Radner equilibrium approach for portfolio allocation and price discovery.
result Radner equilibria uniquely exist and provide solutions for market equilibria.
RI-DeepONet learns neural operators from arbitrary sensor data.
problem Discretization of input functions limits practical applications of DeepONet.
method Introduces RI-DeepONet and two dictionary learning algorithms for INRs.
result RINO handles arbitrary sensor data robustly and applies to various problems.
Deep learning upscales geologic models efficiently.
problem Upscaling large-scale geologic models for efficient simulation.
method Theory-guided convolutional neural network (TgCNN) trained to approximate hydraulic conductivity relationships.
result Deep learning method achieves equivalent upscaling accuracy to numerical methods but with significantly improved efficiency.
SR-NAM maps low-res images to multiple high-res images realistically.
problem Mapping low-resolution images to multiple high-resolution images realistically.
method SR-NAM using Non-Adversarial Mapping (NAM) technique and a degradation model.
result Realistic degradation and down-sampling of high-resolution images.
Deep learning speeds up whole heart MRI to 30 seconds.
problem Long acquisition times in whole heart MRI.
method Deep learning, specifically a 3D residual U-Net, to reconstruct high-resolution images from low-resolution data.
result Super-resolution images show better edge sharpness and fewer artefacts than low-resolution images.
Improved probabilistic solar irradiance forecasting models for grid integration.
problem Enhancing accuracy of solar irradiance forecasts for grid integration.
method Developed and calibrated probabilistic models using post-hoc calibration techniques.
result NGBoost model with CRUDE calibration achieves comparable performance to numerical weather prediction models.
Generative models improve for multiscale scientific data with new noise and interpolation techniques.
problem Numerical challenges in generating high-fidelity samples for multiscale scientific data.
method Design of noise distributions and interpolation schedules in function space to ensure Lipschitz regularity and finite noise roughness.
result Scale-adaptive noise and interpolation schedules improve numerical efficiency and fidelity of generated samples.
Novel algorithm accelerates PnP methods for image deblurring and super-resolution.
problem Efficiently solving inverse problems and imaging with provable convergence guarantees.
method Incorporates quasi-Newton steps into provable PnP framework based on proximal denoisers.
result 2--8x faster convergence compared to other provable PnP methods with similar quality.
Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the super-replication price is the viscosity solution of a fully non-linear parabolic equatio…
We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-paramete…
Numerical models based on physics represent the state-of-the-art in earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model resolutions overwhelms the latest-generation computers, reducing the ability of …
The paper proposes a method to improve fine-resolution predictions using coarse-resolution data.
problem Limited supervision for fine-resolution predictions with scarce data.
method Attention-based regularization on multi-view coarse-resolution data.
result The method improves fine-resolution predictions using coarse-resolution data.
The point of the paper is to show some limitations of geometrical optics in the analysis of subwavelength focusing. We analyze the resolution of the image of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab lens. The former optical medium is deduced from the stereographic projection of a virt…
This study prioritizes temporal resolution over spatial in energy systems models due to higher influence.
problem The impact of spatial and temporal resolution on energy system models.
method Global sensitivity analysis to compare structural aspects, spatial, and temporal resolution.
result Temporal resolution has a higher influence on all results parameters compared to spatial resolution.
Deep learning improves 3D microscopy resolution without matched target images.
problem Anisotropic resolution in volumetric fluorescence microscopy.
method Cycle-consistent generative adversarial network trained on unpaired 2D images.
result Enhanced axial resolution and restored details between imaging planes.
There are 2^n possible resolutions of a smooth pseudodiagram with n precrossings. If we consider piecewise-linear (PL) pseudodiagrams and resolutions that themselves are PL, certain resolutions of the pseudodiagram may not exist in three-space. We investigate this situation and its impact on the weighted resolution set…
Recently M. Kreck introduced a class of stratified spaces called p-stratifolds [M. Kreck, Stratifolds, Preprint]. He defined and investigated resolutions of p-stratifolds analogously to resolutions of algebraic varieties. In this note we study a very special case of resolutions, so called optimal resolutions, for p-str…
New method improves sampling from non-convex distributions using HFHR dynamics.
problem Sampling from non-log-concave densities with non-convex potential functions.
method Hessian-free high-resolution dynamics (HFHR) with reflection/synchronous coupling.
result HFHR dynamics converges faster than kinetic Langevin dynamics (KLD) for non-convex potentials.